Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-14T04:49:42.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing all S-integral points on elliptic curves

Published online by Cambridge University Press:  01 November 1999

ATTILA PETHŐ ,
HORST G. ZIMMER ,
JOSEF GEBEL  and
EMANUEL HERRMANN
ATTILA PETHŐ
Affiliation:
Institut of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, P.O. Box 12, Hungary
HORST G. ZIMMER
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
JOSEF GEBEL
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
EMANUEL HERRMANN
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Let the elliptic curve E be defined by the equation

formula here

with a1, …, a6 ∈ ℤ. Define a finite set of places S = {q1, …, qs−1, qs = ∞} of ℚ and put Q = max {q1, …, qs−1}. Let E(ℚ) denote the set of (x, y) ∈ ℚ2 satisfying (1) and the infinite point [Oscr ].

The multiplicative height of a rational point P = (x, y) ∈ E(ℚ) is defined as the following product over all places q of ℚ (including q = ∞):

formula here

where the [mid ]x[mid ]qs are the normalized multiplicative absolute values of ℚ corresponding to the places q.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 3 , November 1999 , pp. 383 - 402
Copyright
© The Cambridge Philosophical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)